Discussion
What is the remainder when \(67^{67} + 67\) is divided by 68?
Answer: B
Let's analyze the expression in two parts modulo 68. Part 1: \(67^{67} \pmod{68}\). We can write 67 as (68 - 1). So, \((68-1)^{67} \pmod{68}\). This is equivalent to \((-1)^{67} \pmod{68}\), which is -1. Part 2: \(67 \pmod{68}\) is 67. Adding the remainders: \(-1 + 67 = 66\). The remainder is 66.
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